M. Alducin, R. Díez Muiño, J. I. Juaristi

Contents Lecture 1 INTRODUCTION: SURFACE CHEMISTRY AND HETEROGENEOUS CATALYSIS Lecture 2 MOLECULAR STRUCTURE Lecture 3 ELECTRONIC AND STRUCTURAL PROPERTIES OF SURFACES Lecture 4 ELEMENTARY CHEMICAL PROCESSES AT SURFACES: POTENTIAL ENERGY SURFACES Lecture 5 THEORY OF GAS/SURFACE DYNAMICS Lecture 6 COMPUTATIONAL METHODS TO SIMULATE GAS/SURFACE DYNAMICS

Lectures on Molecular Dynamics at Surfaces: Friday May 7th: > theoretical background Tuesday May 11th : > Wednesday May 12th : > Friday May 14th : > st exercise: analysis of N 2 /W(110) PES 2 nd exercise: dissociation dynamics of N 2 on W(110)

Lectures on Molecular Dynamics at Surfaces: Friday May 7th: > theoretical background Tuesday May 11th : > st exercise: analysis of N 2 /W(110) PES Friday May 14th : > nd exercise: dissociation dynamics of N 2 on W(110) 2nd option!!

I.- Theoretical background

Simulation (computer experiments): Experiment: a system is subjected to measurements and a result, in numerical form, is obtained. Theory: In the past, a model of the system was constructed and later validated by checking its ability to describe the behavior of the system in some limit cases (simplification  understanding). Simulation: The advent of powerful computational resources has brought the possibility to reduce the approximations, reproduce the complexity of experimental conditions, and accurately compare with experimental results (study of regions not accesible experimentally).

Physical and chemical processes at surfaces are dynamical in nature -Theoretically, static properties are usually accurately described (ground state): Density Functional Theory, Quantum Chemistry, Quantum Monte Carlo, etc. - Dynamic properties still require further theoretical development (may involve excited states)

gas/surface dynamics dissociative adsorption molecular adsorption desorption some elementary reactive processes at surfaces from the fundamental point of view, the goal is to understand how solid surfaces and nanostructures can be used to promote gas-phase chemical reactions

Langmuir-Hinshelwood Recombination Eley-Rideal recombination gas/surface dynamics

Physical and chemical processes at surfaces are dynamical in nature -Theoretically, static properties are usually accurately described (ground state): Density Functional Theory, Quantum Chemistry, Quantum Monte Carlo, etc. - Dynamic properties still require further theoretical development (may involve excited states)

Lawrence Livermore National Laboratory

Molecular Dynamics Molecular dynamics is a computer simulation technique in which the time evolution of a set of interacting atoms is followed by integrating their equations of motion.

Some nomenclature Classical Molecular Dynamics Simulation: A model of inteeractions between atoms is supplied as input before a simulation can be carried out. Quantum Molecular Dynamics Simulation: They do not require any a priori knowledge of interatomic interactions. Only the laws of quantum mechanics are used. Classical dynamics of nuclei Quantum dynamics of nuclei

gas/surface dynamics dissociative adsorption molecular adsorption desorption some elementary reactive processes at surfaces from the fundamental point of view, the goal is to understand how solid surfaces and nanostructures can be used to promote gas-phase chemical reactions

Langmuir-Hinshelwood Recombination Eley-Rideal recombination gas/surface dynamics

The adiabatic approximation A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum Sketch: Potential energy curves of a neutral diatomic molecule R and its negative ion R -

The adiabatic approximation

Validity of the adiabatic approximation Notes from Ballentine’s book

Ballentine’s book

Molecular Dynamics Molecular dynamics is a computer simulation technique in which the time evolution of a set of interacting atoms is followed by integrating their equations of motion.

Born – Oppenheimer approximation

The Born-Oppenheimer approximation

Quantum dynamics of nuclei are also possible (time-dependent wave-packet propagation, for instance) … but numerically VERY demanding!

Quantum dynamics of nuclei are also possible (time-dependent wave-packet propagation, for instance) … but numerically VERY demanding! Díaz et al., PRB 72, (2005) Dissociation probability of H 2 /Pd(111)

Classical dynamics: In practice…

A list of molecular dynamics packages, for those interested: Molecular Dynamics

Classical Molecular Dynamics Potential Energy Surface (PES) The PES provides the energy (and its derivatives!) for all positions of the nuclei R i. It is a 3N dimensional function!

Classical Molecular Dynamics Potential Energy Surface (PES) The PES provides the energy (and its derivatives!) for all positions of the nuclei R i. It is a 3N dimensional function! Frozen Surface: In our case, everything is reduced to a 6D problem!

How to calculate the forces (the PES)? ‘Classical’ calculation of the PES: - Force fields, parametrizations, etc. Complete quantum calculation of the PES (previous to the dynamics): - Ab-initio methods (DFT, HF, etc.) with ensuing fitting On-the-fly methods: - Ab-initio molecular dynamics - Car-Parrinello

How to calculate the forces (the PES)? ‘Classical’ calculation of the PES: - Force fields, parametrizations, etc. Complete quantum calculation of the PES (previous to the dynamics): - Ab-initio methods (DFT, HF, etc.) with ensuing fitting On-the-fly methods: - Ab-initio molecular dynamics - Car-Parrinello All of them are adiabatic (ground-state) methods! Non-adiabatic methods (TDDFT, for instance) required for excited systems.

Excitation of electron-hole pairs in a metal surface (no gap for excitations) Non-adiabatic processes bulk metal electrons at the surface can be excited

description of electronic excitations by a friction coefficient classical equations of motion m i (d 2 r i /dt 2 )=-dV(r i,r j )/d(r i ) –  (r i )(dr i /dt) for each atom “i” in the molecule friction coefficient adiabatic force: 6D DFT PES - damping of adsorbate vibrations: Persson and Hellsing, PRL49, 662 (1982) - dynamics of atomic adsorption Trail, Bird, et al., JCP119, 4539 (2003) previously used for: friction coefficient: effective medium approximation n(z) z n0n0 bulk metal n0n0  =n 0 k F  tr (k F ) effective medium: FEG with electronic density n 0

Desorption induced by electronic processes (DIET) Non-adiabatic processes MGR process: the molecule is excited to a repulsive PES without any change in the position and momenta of the molecule Antoniewicz process: the excited molecule moves towards the surface and decays into the ground state with higher kinetic energy available

II.- Particular case: dissociation of diatomic molecules on metal surfaces

centro de física de materiales CFM What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. A+B  P direct reaction A+B+C  P+C catalyzed reaction A and B are reactants C is the catalyst P is the reaction product A+B P gas/solid interfaces and heterogeneous catalysis

centro de física de materiales CFM What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. A+B  P direct reaction A+B+C  P+C catalyzed reaction A and B are reactants C is the catalyst P is the reaction product A+B P gas/solid interfaces and heterogeneous catalysis Heterogeneous catalysis: The catalyst is in a different phase  solid surfaces.

centro de física de materiales CFM What is catalysis? The effect produced in facilitating a chemical reaction, by the presence of a substance, which itself undergoes no permanent change. A+B P gas/solid interfaces and heterogeneous catalysis Heterogeneous catalysis: The catalyst is in a different phase  solid surfaces. The chinese symbol for catalyst is the same as the one for marriage broker (matchmaker)

centro de física de materiales CFM ammonia synthesis: 3H 2 (g) + N 2 (g) ↔ 2NH 3 (g) (catalyzed by Fe surface) global context: chemical industry world production: 130 million tons (year 2000), ~200US$/ton

centro de física de materiales CFM Catalysis in car industry: In car engines, CO, NO, and NO 2 are formed. Catalytic converters reduce such emissions by adsorbing CO and NO onto a catalytic surface, where the gases undergo a redox reaction. CO 2 and N 2 are desorbed from the surface and emitted as relatively harmless gases: 2CO + 2NO → 2CO 2 + N 2 global context: car industry

Molecular beam techniques Sticking Coefficient The sticking coefficient, S, is a measure of the fraction of incident molecules which adsorb upon the surface i.e. it is a probability and lies in the range 0 - 1, where the limits correspond to no adsorption and complete adsorption of all incident molecules respectively. In general, S depends upon many variables i.e. S = f ( surface coverage, temperature, crystal face.... )  EiEi  Sticking coefficient of O2 on Ag(111): dependence on energy and polar incidence angle

Molecular beam techniques Molecular beam scattering studies of H2– D2 exchange on Pt332 surface, showing that atomic steps on metal surfaces break chemical bonds, in this case, hydrogen-hydrogen bonds, with unit reaction probability (a) schematic defining the geometry of the incident angle polar and azimuthal of the molecular beam with respect to a stepped surface. (b) HD production as a function of angle of incidence of the molecular beam normalized to the incident D2 intensity.

x y z surface unit cell   X Y Z  EiEi   Incidence conditions are fixed: (E i,   Monte-Carlo sampling on the internal degrees of freadom: (X, Y, ,  ) and on  (parallel velocity)  Born-Oppenheimer approximation  Frozen surface approximation  6D PES: V(X, Y, Z, r, ,  ) Calculation of the Potential Energy Surface (PES) Classical trajectory calculations

The test system for our exercises will be N 2 on W surfaces. Why?

W: Wolfram or Tungsten W was first isolated in 1783 by Fausto and Juan José Elhuyar, two Spanish chemists working in the Basque Country. The Elhuyar brothers named the element 'volfram', from the mineral from which it was extracted. But the name 'tungsten', of Swedish origin, is the one that has prevailed. centro de física de materiales CFM

sticking coefficient S 0 W(100) T=800K T=300K T=100K impact energy E i (eV) W(110) T=800K no thresholdthreshold normal incidence Rettner et al. (1988) Beutl et al. (1997) Pfnür et al. (1986) Rettner et al. (1990) measurements of N 2 dissociation on W surfaces centro de física de materiales CFM

surface face and reactivity - surface roughness (work function) - unique active sites at the surface two possible reasons for the difference in reactivity over different faces: the rate-limiting step in ammonia formation is the dissociative adsorption of N 2 on the surface centro de física de materiales CFM

surface face and reactivity - surface roughness (work functions) - unique active sites at the surface two possible reasons for the difference in reactivity over different faces: the rate-limiting step in ammonia formation is the dissociative adsorption of N 2 on the surface most reactive surfaces have C 7 sites (seven nearest neighbors) centro de física de materiales CFM

W(100) W(110) adsorption energy DFT = 7.4 eV Exp. = eV adsorption distance DFT = 0.63 Å adsorption energy DFT = 6.8 eV Exp. = 6.6 eV adsorption distance DFT = 1.15 Å final state features: N adsorption on W centro de física de materiales CFM

sticking coefficient S 0 W(100) T=800K T=300K T=100K impact energy E i (eV) W(110) T=800K no thresholdthreshold normal incidence Rettner et al. (1988) Beutl et al. (1997) Pfnür et al. (1986) Rettner et al. (1990) measurements of N 2 dissociation on W surfaces activation barrier? centro de física de materiales CFM

6D potential energy surface (PES) of N 2 /W(110) - DFT - GGA (PW91) calculation with VASP - Plane-wave basis set and US pseudopotentials - periodic supercell: 5-layer slab and 2x2 surface cell - 30 configurations = 5610 ab-initio values - interpolation through the corrugation reducing procedure [Busnengo et al., JCP 112, 7641 (2000)] centro de física de materiales CFM

 = 45 o  = 270 o  = 90 o  125 o  = 90 o  54 o =0o=0o Definition of System of coordinates for N 2 /W(110) centro de física de materiales CFM

 = 45 o  = 270 o  = 90 o  125 o  = 90 o  54 o =0o=0o r(Å) Z(Å) some elbow plots for the N 2 /W(110) system distance between contour lines = 0.2eV E<0 E>0 E=0 centro de física de materiales CFM

classical dynamics - classical trajectory method - adiabatic description (no dissipation) centro de física de materiales CFM